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In short order Hermite then proceeds to solve the general
equation of the fifth degree, using for the purpose elliptic func-
tions (strictly, elliptic modular functions, but the distinction is
of no importance here). It is almost impossible to convey to a
non-mathematician the spectacular brilliance of such a feat; to
give a very inadequate simile, Hermite found the famous 'lost
chord* when no mortal had the slightest suspicion that such an
elusive thing existed anywhere in tune and space. Needless to
say his totally unforeseen success created a sensation in the
mathematical world. Better, it inaugurated a new department
of algebra and analysis in which the grand problem is to dis-
cover and investigate those functions in terms of which the
general equation of the rath degree can be solved explicitly in
finite form. The best result so far obtained is that of Hermite* s
pupil, Poincar6 (in the ISSCTs), who created the functions giving
the required solution. These turned out to be a 'natural'
generalization of the elliptic functions. The characteristic of
those functions that was generalized was periodicity. Further
details would take us too far afield here, but if there is space
we shall recur to this point when we reach Poincare.

Hermite's other sensational isolated result was that which
established the transcendence (explained in a moment) of the
number denoted in mathematical analysis by the letter e>

where 1! means 1, 2! = 1 x 2, 3! = 1 x 2 x 3, 4! ='1 X 2
X 3 x 4, and so on; this number is the "base' of the so-called
'natural* system of logarithms, and is approximately
2-71828182S ____ It has been said that it is impossible to con-
ceive of a universe in which e and IT (the ratio of the circum-
ference of a circle to its diameter) are lacking. However that
may be (as a matter of fact it is .false), it is a fact that e turns up
everywhere in current mathematics, pure and applied. Why
this should be so, at least so far as applied mathematics is con-
cemed5 may be inferred from the following fact: e*, considered
as a function of a?, is the only function of re whose rate of change